The most exact calculation would be to know when this feat takes place, since the moon doesn't just stay an exact amount away from the Earth, but rather gets closer or moves father depending on the time of year because the orbit isn't a perfect circle.
But on average, the moon is 238,855 miles away from Earth
according to NASA, which is 384,399,861.1 meters away, or 384,399.8611 km from Earth. Then you just divide by 1 because it only takes one second and you get 384,399 km/s, which is FTL.